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<H1>Dissertation Research Overview</H1>

<H2>THIS PAGE IS CURRENTLY UNDER CONSTRUCTION!!! </H2>

<P>The overall theme of my research is reasoning with and refining imprecise
models of physical processes. Because we cannot know the world precisely,
imprecision is implicit in any modeling task. However, it is often the
case that imprecision is simply ignored since it has no place in many existing
modeling and simulation methodologies. Sometimes, this is of no consequence,
but in other cases, the mismatch between prediction and true behavior may
lead to erroneous conclusions. In fields where imprecision is addressed
(for example, in robust control), the methods are often resticted in terms
of the types of imprecision allowed or are not guaranteed to produce all
the predictions inherent in the model or produce predictions that are too
weak to provide useful guidance. What is needed is a general method for
representing and reasoning with imprecison that can capture the typical
types of imprecision inherent in modeling tasks and can produce predictions
that maintain precision consistent with the model imprecision. In the <!WA0><A HREF="http://www.cs.utexas.edu/users/bert/sqsim.html">next
section</A>, I describe SQSim, a representation and simulation method that
meets these goals. </P>

<P>While imprecision is inherent in any modeling task, it is also true
that a model's precision can be improved with experience with the underlying
physical process. Learning a model from a combination of prior knowledge
and empirical data is the task of system identification. Typically, identification
methods work under the assumption that a parametric model of the process
exists and searches the model space for the precise model that best matches
the empirical data. Confidence bounds on the parameters (and hence the
prediction) can also be determined to represent the uncertainty inherent
in using a finite amount of data. This method can be quite efficient in
cases where the search space has good properties (such as an easily computable
gradient). For cases where this does not hold, however, (for example, if
we allow functional as well as parametric uncertainty), finding an optimal
model may be very difficult. In addition, identification methods require
that empirical data be informative enough to provide complete experience
with the system over the desired operating range. If such conditions cannot
be met, the resulting model may differ greatly from the true model. In
the <!WA1><A HREF="http://www.cs.utexas.edu/users/bert/squid.html">third section</A>,
I describe SQUID, a method for refining an existing model by using possibly
uninformative data. </P>

<P>SQSim and SQUID provide two key technologies for automating the model-building
task. By combining them with a method for postulating initial qualitative
models from data, one could construct a system that can automatically construct
models using a combination of empirical and prior knowledge.</P>

<P><!WA2><A HREF="http://www.cs.utexas.edu/users/bert/index.html">BKay </A></P>

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